Universal Access To All Knowledge
Home Donate | Store | Blog | FAQ | Jobs | Volunteer Positions | Contact | Bios | Forums | Projects | Terms, Privacy, & Copyright
Search: Advanced Search
Anonymous User (login or join us)
Search Results
Results: 1 through 3 of 3 (0.003 secs)
You searched for: creator:"Jacob Korevaar"
[texts]Prime pairs and Zeta's zeros - Jacob Korevaar
There is extensive numerical support for the prime-pair conjecture (PPC) of Hardy and Littlewood (1923) on the asymptotic behavior of pi_{2r}(x), the number of prime pairs (p,p+2r) with p not exceeding x. However, it is still not known whether there are infinitely many prime pairs with given even difference! Using a strong hypothesis on (weighted) equidistribution of primes in arithmetic progressions, Goldston, Pintz and Yildirim have shown (2007) that there are infinitely many pairs of primes d...
Downloads: 1
[texts]Ikehara-type theorem involving boundedness - Jacob Korevaar
Consider any Dirichlet series sum a_n/n^z with nonnegative coefficients a_n and finite sum function f(z)=f(x+iy) when x is greater than 1. Denoting the partial sum a_1+...+a_N by s_N, the paper gives the following necessary and sufficient condition in order that (s_N)/N remain bounded as N goes to infinity. For x tending to 1 from above, the quotient q(x+iy)=f(x+iy)/(x+iy) must converge to a pseudomeasure q(1+iy), the distributional Fourier transform of a bounded function...
Downloads: 13
[texts]Lower bound for the remainder in the prime-pair conjecture - Jacob Korevaar
For any positive integer r, let pi_{2r}(x) denote the number of prime pairs (p, p+2r) with p not exceeding (large) x. According to the prime-pair conjecture of Hardy and Littlewood, pi_{2r}(x) should be asymptotic to 2C_{2r}li_2(x) with an explicit positive constant C_{2r}. A heuristic argument indicates that the remainder e_{2r}(x) in this approximation cannot be of lower order than x^beta, where beta is the supremum of the real parts of zeta's zeros...
Downloads: 5
Advanced search

Group results by:

> Relevance

Related creators

Jacob Korevaar

Related mediatypes


Terms of Use (10 Mar 2001)